64.10.19 problem 19

Internal problem ID [13425]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 05:42:15 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x$5)-2*diff(y(x),x$4)+diff(y(x),x$3)=0,y(x), singsol=all)
 

\[ y = \left (x c_5 +c_4 \right ) {\mathrm e}^{x}+c_{3} x^{2}+c_{2} x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 30

DSolve[D[y[x],{x,5}]-2*D[y[x],{x,4}]+D[y[x],{x,3}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (c_2 (x-3)+c_1)+x (c_5 x+c_4)+c_3 \]